Geodesic
Stationary solutions for the Cahn--Hilliard equation coupled with Neumann boundary conditions
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 60-74

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The structure of stationary states of the one-dimensional Cahn–Hilliard equation coupled with the Neumann boundary conditions has been studied. Here the free energy is given by a fourth order polynomial. The bifurcation diagram for existence and uniqueness of monotone solutions for this problem has been constructed. Namely, we find the length of the interval on which the solution monotonically increases or decreases and has one zero for some fixed values of physical parameters. Under the non-uniqueness we understand a possibility of existence of more than one monotone solutions for the same values of physical parameters.
Keywords: the Cahn–Hilliard equation; Neumann boundary conditions; steady states. 
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     title = {Stationary solutions for the {Cahn--Hilliard} equation coupled with {Neumann} boundary conditions},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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I. B. Krasnyuk; R. M. Taranets; M. Chugunova. Stationary solutions for the Cahn--Hilliard equation coupled with Neumann boundary conditions. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 60-74. http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a5/